The analytic-functional calculus for several commuting operators

Taylor, Joseph L.

doi:10.1007/bf02392329

Cited by 265 publications

(177 citation statements)

References 11 publications

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“…In this section we briefly review Taylor's definition of the joint spectrum for n-tuples of bounded commuting operators as discussed in [17]. In addition we discuss some related material which will be required below.…”

Section: The Joint Spectrum Of Several Commuting Operatorsmentioning

confidence: 99%

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Multiparameter spectral theory and Taylor's joint spectrum in Hilbert space

Rynne¹

1988

Proceedings of the Edinburgh Mathematical Society

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Let n≧1 be an integer and suppose that for each i= 1,…,n, we have a Hilbert space Hi and a set of bounded linear operators Ti, Vij:Hi→Hi, j=1,…,n. We define the system of operatorswhere λ=(λ1,…,λn)∈ℂn. Coupled systems of the form (1.1) are called multiparameter systems and the spectral theory of such systems has been studied in many recent papers. Most of the literature on multiparameter theory deals with the case where the operators Ti and Vij are self-adjoint (see [14]). The non self-adjoint case, which has received relatively little attention, is discussed in [12] and [13].

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Section: The Joint Spectrum Of Several Commuting Operatorsmentioning

confidence: 99%

“…We define the commuting tuples Thus the result follows from the spectral mapping theorem for the analytic functional calculus for sets of commuting operators (see [17]). …”

Section: Corollary 44 Suppose That the Array [Vy] Is Commutative Anmentioning

confidence: 99%

Multiparameter spectral theory and Taylor's joint spectrum in Hilbert space

Rynne¹

1988

Proceedings of the Edinburgh Mathematical Society

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“…Assume that y eΐR(T \ Z), hence y = lim n y n , with y n e 3t(T\Z) 9 for any natural n. We may suppose that Σ»=ill2/n+i -Vn\\ < + °° and proceed as in the proof of Theorem 2.2. Namely, for any a we can choose a sequence x n , a e 3D(T| Z a ) such that Tx Ua …”

Section: Suppose That X Y Are the Duals Of The Banach Spaces X* Y* mentioning

confidence: 99%

“…4. First of all we recall the definition of the joint spectrum of a commuting system T = (T u , T n ) c S5(X), in the sense of Taylor's [9] (see also [12] …”

Section: Suppose That X Y Are the Duals Of The Banach Spaces X* Y* mentioning

confidence: 99%

The closed range modulus of operators

Vasilescu¹

1975

Pacific J. Math.

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“…, z n − T n ) is not invertible. It was a breakthrough [12] when J.L.Taylor introduced this notion of joint spectrum and showed that it carries an analytic functional calculus, that is, there exists a continuous algebra homomorphism…”

Section: Introductionmentioning

confidence: 99%

Samuel multiplicity and Fredholm theory

Eschmeier

2007

Math. Ann.

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Abstract. In this note we prove that, for a given Fredholm tuple T = (T1, . . . , Tn) of commuting bounded operators on a complex Banach space X, the limits cp(T ) = lim k→∞ dim H p (T k , X)/k n exist and calculate the generic dimension of the cohomology groups H p (z − T, X) of the Koszul complex of T near z = 0. To deduce this result we show that the above limits coincide with the Samuel multiplicities of the stalks of the cohomology sheaves H p (z −T, O X C n ) of the associated complex of analytic sheaves at z = 0.

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The analytic-functional calculus for several commuting operators

Cited by 265 publications

References 11 publications

Multiparameter spectral theory and Taylor's joint spectrum in Hilbert space

Multiparameter spectral theory and Taylor's joint spectrum in Hilbert space

The closed range modulus of operators

Samuel multiplicity and Fredholm theory

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